In previous work the investigator has developed the Disturbed Highest Derivative Polynomial (DHDP) as a model-free time curve and has published the theoretical development for its use as the overall time curve in a linear Gaussian model for longitudinal data with fixed covariate effects and autocorrelated errors but without subject effects. The aim of this proposal is to enhance analysis statistical methods for epidemiological studies by extending this development to models for binary-logistic and Poisson data and by including random subject effects in the Gaussian model. For the logistic model, the DHDP would replace the constant which appears in the log odds in the non-longitudinal case. The first-order DHDP is a straight line whose slope receives random disturbances over time. As such it capable of fitting a rich variety of arbitrarily changing time curves. The second-order DHDP would generally provide a fit with smaller high frequency variation. There are a number of longitudinal data analysis methods currently available for Gaussian and binary-logistic data. They all have in common the requirement to explicitly model the overall time curve--usually by a low order deterministic polynomial. The main significance of this proposal will be to represent the overall time curve by a DHDP, thereby allowing the possibility for fitting arbitrarily changing time curves without explicitly modeling the form of the change over time. The order of the DHDP can be selected by a modification of the Akaike Information Criterion. The Poisson model will be useful in fitting the periodic reported incidence of a rare disease. The relationship of the DHDP to the Smoothing Polynomial Spline (SPS) will be shown and methods will be developed for using a SPS instead of a DHDP in analysis. Robustness of the methods will be examined by computer simulation studies which will evaluate and compare the ability of the DHDP and SPS models to estimate covariate effects and time curves when the time curves are generated by processes other than DHDP.